= Membrane potential
{title2=$V=V_{\mathrm{inside}}-V_{\mathrm{outside}}$}
{wiki}
A <membrane potential> is an <electric potential difference> across a <cell membrane>. We use the convention
$$
V_m=\phi_{\mathrm{inside}}-\phi_{\mathrm{outside}}.
$$
Taking the external <electric potential> as zero makes $V_m<0$ mean that the inside is at lower <electric potential>. “Negative inside” describes a difference, not an absolute <electric potential>, and does not imply that the entire <cytosol> has a large net negative <electric charge>.
Consider a <cell membrane> permeable only to <potassium> <ions>, with higher <potassium> <concentration> inside. <Diffusion> initially favors outward transport. If balancing negative <ions> cannot follow, that loss of positive <electric charge> produces a small inner excess of negative <electric charge> and an outer positive excess. The resulting <electric field> favors inward <potassium> transport. At the <Nernst equilibrium potential>, chemical and electrical contributions to <electrochemical potential> balance; <ions> still cross both ways, with zero net transport.<Molecular Biology of the Cell, 4th edition by Bruce Alberts and others/Ion Channels and the Electrical Properties of Membranes>[Molecular Biology of the Cell, 4th edition by Bruce Alberts and others; The Resting Membrane Potential Is Determined Mainly by K+ Leak Channels in Most Animal Cells: selective potassium passage and opposing electrical influence]{ref}
\Image[/membrane-potential-forces-and-electrodes.png]
{title=Opposing influences on <potassium> transport and the sign of an intracellular voltage recording}
{description=Original conceptual diagrams: a selective <cell membrane> with $V_m<0$, and an intracellular <electrode> compared with an external <reference electrode> in seawater. The recording diagram illustrates connections and sign, not a historical apparatus reconstruction or a measured trace. Arrows indicate transport tendencies; particle numbers and distances are schematic.}
In living <biological cells>, several <ions> can permeate and pumps maintain their <concentration> differences through <active transport>. Pumps transporting net <electric charge> also contribute <electric current>. Thus $V_m=E_{\mathrm K}$ is a special limit, not a universal rule; <membrane potential> need not always be negative.<Molecular Biology of the Cell, 4th edition by Bruce Alberts and others/Ion Channels and the Electrical Properties of Membranes>[Molecular Biology of the Cell, 4th edition by Bruce Alberts and others; K+ leak-channel discussion; The Resting Potential Decays Only Slowly When the Na+-K+ Pump Is Stopped; action-potential discussion]{ref} The existing <reversal potential> example shows how opposing <electric currents> can balance without each <ion> reaching <thermodynamic equilibrium>. This makes <selective permeability> a way to convert chemical differences into electrical signals: changing the available <ion channels> changes which <electrochemical gradients> influence the voltage.
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